Achievement of Minimum Seismic Damage for Zipper Braced Frames Based on Uniform Deformations Theory

Transcription

1 Journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43- journal homepage: Achevement of Mnmum Sesmc Damage for Zpper Braced Frames Based on Unform Deformatons Theory J. Vasegh Amr 1*, M. Esmaelna Amr and B. Ganjav 3 1. Assocate Professor, Faculty of Cvl Engneerng, Babol Unversty of Technology, Babol, Iran.. Ph.D. Student, Faculty of Cvl Engneerng, Babol Unversty of Technology, Babol, Iran. 3. Assstant Professor, Department of Cvl Engneerng, Unversty of Mazandaran, Babolsar, Iran. Correspondng author: vasegh@nt.ac.r ARTICLE INFO Artcle hstory: Receved: 5 June 15 Accepted: 13 January 1 Keywords: Zpper-braced Frame structures, Maxmum damage, Unform ductlty dstrbuton, Inelastc behavor, Severe ground exctaton. ABSTRACT When structures are subjected to severe ground exctatons, structural elements may be prone to yeldng, and consequently experence sgnfcant levels of nelastc behavor. The effects of nelastc behavor on the dstrbuton of peak floor loads are not explctly accounted for n current sesmc code procedures. Durng recent years, many studes have been conducted to develop new desgn procedures for dfferent types of buldngs through proposng mproved desgn lateral load patterns. One of the most mportant parameters of structural damage n performance-based sesmc desgn s to lmt the extent of structural damages (maxmum nter-story ductlty rato) n the system and dstrbute them unformly along the heght of the structures. In ths paper, a practcal method s developed for optmum sesmc desgn of zpper-braced frames (ZBF) subjected to sesmc exctatons. More effcent desgn s obtaned by redstrbutng materal from strong to weak parts of a structure untl a state of unform ductlty rato (damage) prevals. By applyng the proposed desgn algorthm on 5, 1 and 15 storey zpper-braced frames subjected to 1 synthetc sesmc exctatons, the effcency of the proposed method s nvestgated for specfc synthetc sesmc exctatons. The results ndcate that, for a constant structural weght, the structures desgned accordng to the proposed optmzaton algorthm experence up to 5% less global ductlty rato (damage) compared wth code-based desgn structures. 1. Introducton In the recent earthquakes, the structures desgned based on the new terms of sesmc desgn have an approprate performance n the safety of occupants; however, the extent

2 44 J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43- of damage and economc losses n these structures were unexpected. It s well known that the structures desgned n accordance wth the current sesmc provsons may experence extreme damages under severe earthquakes [1-4]. In the current sesmc desgn codes, lateral-load resstng systems for regular structures may be desgned based on the equvalent lateral force procedure [5-7]. A fundamental component of the equvalent lateral force procedure s the utlzaton of desgn lateral load patterns to determne the strength and the stffness characterstcs of structure. These codespecfed desgn lateral load patterns were set up based on the dynamc behavor of elastc structural systems. Therefore, the desgn lateral load patterns of ths procedure do not explctly account for the nelastc response of the structural system. If the structure s expected to experence sgnfcant levels of nelastcty, code-specfc lateral load dstrbutons may not provde an accurate representaton of the story shear strength demands appled to the structural system. Thus, a desgner has certan control on the amount of the global structural damage experenced by the structure based on an approprate selecton of stffness, strength, and ductlty requrements n the sesmc desgn stages of a structure. However, a desgner has lmted control over the dstrbuton of damage, whch s manly caused by load redstrbuton effects characterstc of nelastc structural response [8]. The total lateral load force proposed by sesmc provsons, s generally less than the actual earthquake forces mposed on structures durng sever earthquakes and consequently the conventonal structures were experenced large deformatons and nonlnearty n strong ground motons. Therefore, the desgn of structures based on elastc vbraton modes s not logcal as the actual earthquake force s a functon of structural dynamc characterstcs such as yeld shear strength and nter-story ductlty rato [9]. Many researchers have recommended mproved sesmc desgn load patterns for multstory structures. Leelatavwat et al. [1] evaluated the sesmc demands of md-rse moment-resstng frames desgned n accordance to UBC 94. They proposed mproved load patterns usng the concept of energy balance appled to moment-resstng frames wth a pre-selected yeld mechansm. Lee and Goel [11] also proposed new sesmc lateral load patterns by usng hgh-rse moment-resstng frames up to -story wth the same concept whch Leelatavwat et al. [1] used. In a more comprehensve research, Mohammad et al. [1] nvestgated the effect of lateral load patterns specfed by the Unted States sesmc codes on drft and ductlty demands of fxed-base shear buldng structures under 1 earthquake ground motons, and found that usng the code-specfed desgn load patterns do not lead to a unform dstrbuton and mnmum ductlty demands. Ganjav et.al [13] nvestgated the effect of equvalent statc and spectral dynamc lateral load patterns specfed by the major sesmc codes on heght-wse dstrbuton of drft, hysteretc energy and damage subjected to severe earthquakes n fxed-base renforced concrete buldngs. More recently, several studes have been conducted by researchers to evaluate and mprove the code-specfed desgn lateral load patterns based on the nelastc behavor of the structures [8, 14-18]. As stated n the lterature, consderable effort have been made on the optmum sesmc

3 J. Vasegh Amr et al./ Journal of Rehabltaton n Cvl Engneerng 3-1 (15) desgn of dfferent types of structures such as shear buldngs, steel and concrete momentresstant frames, concentrcally- and eccentrcally- braced frames and etc. over the last decade. Zpper-braced frame (ZBF) s one of the nnovatve load-resstng systems frst ntroduced by Khatb et al. [19], and developed by other researchers durng the last decade [, 1]. Ths system has a specal sesmc behavor than other loadresstng systems as t depends on bucklng behavor of braces n the heght of the structure. In the present study, a large number of nonlnear dynamc analyses are performed to acheve the unform deformaton over heght of the ZBF models. In ths regard, 5, 1 and 15 story of ZBF models wth dfferent characterstcs whch wll be explaned n the next secton are modeled and the optmzaton technque proposed by and Moghaddam [14] and Ganjav and Hao [17] for shear-buldng systems are modfed and developed for ZBF systems. Based on the proposed optmzaton algorthm and by adoptng the stores ductlty rato as a damage crteron, the dstrbuton of stores ductlty rato over heght of the structures wll be more unform, leadng consderable decrease of the maxmum ductlty rato of ZBF the structure. Fnally, the effcency of the proposed optmzaton algorthm s demonstrated through several examples. It s shown that wth assumpton of constant structural weght, the sesmc performance of such structures s near optmum such that they undergo less global damage when compared to code-based structures.. Structures modelng and assumptons The behavor of concentrcally braced frame (CBF) n chevron confguraton s controlled by the bucklng of the frst story braces n compresson. Ths wll result n a localzaton of the falure and loss of lateral resstance. To overcome the adverse effect of ths behavor, Khatb et al. [19] proposed to lnk all beamto-brace ntersecton ponts of adjacent floors and to transfer the unbalanced load to the vertcal member called zpper column and ths new structural system called zpperbraced frame. The man applcaton of zpper braced frame (ZBF) s to te all braceto-beam ntersecton ponts together, and force all compresson braces n a braced bay to buckle smultaneously. Ths confguraton wll result n a better hysteretc response and more unform energy dsspaton (.e., unform damage dstrbuton) over the heght of the structure. Wth the am of avodng storey mechansm formaton, Sabell [] has carred out a study on the desgn and behavor of ZBF systems. Later on, Tremblay and Trca [] proposed a ZBF system wth elastc zpper columns, whle braces and beams were desgned to undergo plastc deformatons. Smlarly, a ZBF system wth suspended struts was proposed by Yang et al. [1]. Ths system conssts of addng an elastc truss at the top floor level where braces were desgned to behave elastcally n order to avod the full-heght zpper mechansm formaton. All the remanng braces were proportoned to buckle and zppers to yeld. In fact, they proposed a new desgn procedure and confguraton of ZBF system called suspended zpper braced frame (S-ZBF). In ths paper, three zpper-braced frames (ZBFs) models wth 5, 1 and 15 stores wth the fundamental perods of.4,. and.8 sec, respectvely are sesmcally loaded based on ASCE7-1 lateral load pattern [3] and are desgned based on AISC-LRFD [4]. They are then subjected to earthquake

4 4 J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43- ground motons through performng nonlnear dynamc analyses. The geometrc confguratons of these models are shown n Fgure 1. The general formulaton of the lateral load pattern specfed by the ASCE7-1 s defned as [3]: F x 1 T.5 k Wx hx. V ; x 1,,..., n ; k.5t.75 ; T.5.5 n k W h T. 5 1 (1) where F x and V are respectvely the lateral load at level x and the desgn base shear; w and w x are the porton of the total gravty load of the structure located at the level or x; h and h x are the heght from the base to the level or x; n s the number of stores; and k s an exponent that dffers from one sesmc code to another. Fgure 1 shows a typcal ZBF model used n ths study. response of structural and geotechncal systems subjected to earthquakes. To smulate the bucklng behavor of a brace under compresson for the hysteretc response of the zpper frame model, a brace model wth a small ntal mperfecton has been defned []. Fve percent Raylegh dampng was assgned to the frst mode and the mode n whch the cumulatve mass partcpaton was at least 95%. Fgure shows Schematc graph of a brace model n ZBF structures. Fgure. Schematc graph of a brace model. Fgure 1. Typcal ZBF model All the nonlnear dynamc analyses have been performed by OPENSEES [5], whch allows users to create fnte element applcatons for smulatng the. Earthquake records used n ths study To acheve the unform deformatons along the heght of structures, 1 earthquake ground motons wth dfferent characterstcs recorded on very dense sol (sol type C, wth

5 J. Vasegh Amr et al./ Journal of Rehabltaton n Cvl Engneerng 3-1 (15) shear wave velocty between 3 m/s and 75 m/s) accordng to the IBC-1 [] are selected. The man characterstcs of these ground motons are lsted n Table 1. All the selected ground motons are obtaned from earthquakes wth magntude greater than havng closest dstance to fault rupture more than 3 km wthout pulse n velocty tme hstory. To be consstent, usng SesmoMatch [7] software the selected sesmc ground motons are adjusted to the elastc desgn response spectrum of IBC-1 [] wth sol type C. SesmoMatch [7] s an applcaton capable of adjustng earthquake accelerograms to match a specfc target response spectrum usng wavelets algorthm. Fgure 3 shows a comparson of the 1 synthetc ground moton spectra wth the target elastc desgn response spectrum of IBC-1 []. Table1. Selected ground motons sol type C on the bass of USGS ste classfcaton. Earthquake Year Staton Component Dstance (km) Sol Type PGA (g) Borrego Mtn El Centro Array # C.13 Kocael (18) 1999 Iznk C.98 Kocael (9) 1999 Iznk C.13 Landers Palm Sprngs Arport 37.5 C.7 Loma Preta (1) Salnas - John & Work 1 3. C.91 Loma Preta (5) Salnas - John & Work 5 3. C.11 Morgan Hll Hollster Cty Hall C.71 N. Palm Sprngs (7) Hemet Fre Staton C.144 N. Palm Sprngs (3) Hemet Fre Staton C.13 Vctora Chhuahua C.15

6 48 J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43- Sa (g) T (sec) Fgure 3. IBC-1 [] desgn spectrum for sol type C and response spectra of 1 earthquakes (5% dampng) for selected ground motons. 3. Unform deformaton theory Moghaddam and Hajrasoulha [14] showed that usng the common sesmc desgn method would not lead to the unform dstrbuton of ductlty demands over the heght of the structures. They concluded that when the lateral dsplacement ncreases, the strength would generally decrease n nonlnear regon. Therefore, the sesmc performance of such structures can be mproved by substtutng the strong parts of the structure to the weaker ones. Ths causes more unform dstrbuton of deformatons along the heght of the structures and consequently the maxmum (overall) deformaton decreases. Accordng to ths theory, lateral resstant factors of structures can be dstrbuted such that they exhbt more unform deformatons. In fact, the lateral load pattern determnes how the lateral resstant factors should be dstrbuted along the heght of structures. In the present paper, by utlzng ths theory an optmzaton algorthm s developed to obtan a new lateral load pattern to mprove the sesmc performance of zpper-braced frames. 4. Damage ndex In recent years, almost all of the desgn procedures of structures attempted to quanttatvely estmate the earthquakenduced damage n structures. Although the damage caused by the nonlnear response of the structure under earthquake exctaton depends on many factors, for practcal purposes most researchers consder maxmum deformaton as the man factor of structural and non-structural damages [8]. It means that f the maxmum deformaton of structure exceeds from allowable value, the structure wll fal. Some researchers

7 J. Vasegh Amr et al./ Journal of Rehabltaton n Cvl Engneerng 3-1 (15) proposed the stores drft as the damage crtera and some of them preferred stores ductlty, snce the later crteron can take nto account for the energy absorbed by the structure even ndrectly. In ths paper, the storey ductlty has been consdered as the structural damage ndex. In performancebased desgn methods, a structure may be desgned based on two crtera: 1: Mnmum Sesmc Weght wth specfc performance level (target ductlty). : Mnmum Structural Damage wth constant sesmc weght. In the present study, the second procedure s regarded as the optmzaton crteron to reduce the global damage n the structures. The ductlty rato ( ) s defned as the rato of the maxmum value of relatve dsplacement of the story to the yeld dsplacement of a story whch can be presented as follows: max y )( Where max and y are the maxmum nterstory dsplacement demand and the yeld nterstory dsplacement of the same story for a gven earthquake ground moton, respectvely. 5. Proposed procedure to acheve the unform ductlty The adopted ZBF models ntroduced n the prevous sectons are used drectly for nonlnear dynamc analyses. In ZBF systems, lateral resstance (total shear strength) of each story depends on the axal strength of the tenson and compresson braces. When the lateral dsplacement of the structure s ncreased, the tenson brace s yelded and the compresson braces are buckled. Fgure 4 shows the behavor of ZBF systems when subjected to a lateral load. Snce all beams are connected to columns by pn n the ZBF structure, the shear forces of columns are neglgble. Thus, the lateral resstance of each story can be calculated by Equaton (3). Fgure 4. Behavor of a ZBF system under lateral load. V ( Ty Pc n y c cr )cos ( ) A. cos (3) Where V, T y, P c and are the shear strength of th story, yeld strength, bucklng strength and cross secton area of th story braces, respectvely. Accordng to the unform

8 5 J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43- deformaton theory, to obtan the unform dstrbuton of deformatons over the heght of the structure and to reduce the maxmum deformaton n the structure, t s necessary to substtute the strong parts of the structure by the weaker ones. To ths end, the lateral strength of each story should be modfed n an teratve procedure such that the unform dstrbuton of damage along the heght of the structure s acheved. For a gven fundamental perod (T ), t s requred to decrease or ncrease the cross secton area of braces to reach the ductlty rato of each story, as damage crteron, to the average target ductlty rato. However, by changng the cross secton area of ZBF braces, both the dstrbuton of stffness over the heght of the structure and the structural fundamental perod also change. Ths s nconsstent wth the concepton of unform deformaton theory and optmum lateral load pattern. The optmum lateral load pattern can be obtaned by modfyng the stffness or strength of dfferent stores whle the fundamental perod remans constant. In order to obtan the average ductlty rato n each story of the ZBF system for a gven fundamental perod, the braces area moments of nerta (I) are modfed nstead of the braces cross secton area. That s obtaned by changng the geometrc characterstcs of braces secton area as the shear strength of each story (V ) depends on yeld and crtcal stresses of braces (.e., ( y ) and ( cr ) n Equaton (3)). In other words, the yeld stress ( y ) of the braces depends on the materal propertes of braces whle ndependent of the geometrc characterstcs of braces secton. The crtcal stress ( cr ) of the braces, however, s related to both aforementoned parameters through slenderness rato parameter (). As a result, any modfcaton n the story shear strength can be done by alterng the slenderness rato of the braces wthout any changes n fundamental perod of vbraton as follows: E E A.( KL) cr. I )4( By substtutng the Eq. (4) n Eq. (3): E V n y A cos c cos ( KL) A cos 1 n V. I y E c cos ( KL) 1 V I I )5( Equaton (5) shows that f the total cross sectonal area of braces s to be constant, the shear strength of each story would depend on the braces area moment of nerta. By utlzng ths strategy, the fundamental perod of the ZBF system wll be constant and thus t s possble to change the lateral strength of each story (.e., base shear) to acheve the average ductlty rato smultaneously. In the present study, the proposed method by Moghadam and Hajrsoulha [14] for shear buldng systems s developed for ZBF systems to reduce the maxmum global damage and to obtan the unform dstrbuton of ductlty rato along the heght of the structure n order to mnmze the teraton steps: 1. Desgn the ZBF model based on the ASCE7-1 [3] lateral load pattern.. Select an earthquake ground moton. 3. Select a fundamental perod of structure, and scale the total stffness wthout alterng the stffness dstrbuton pattern such that the structure has a specfed target fundamental perod based on proposed Equatons of 4 and 5. Snce the fundamental perod of structure drectly depends on cross secton area of braces, the followng equaton s used for scalng the stffness to reach the target perod by just one step:

9 J. Vasegh Amr et al./ Journal of Rehabltaton n Cvl Engneerng 3-1 (15) ( T A j ) 1.( Aj ) T t arg et () Where A j, T and T target are the cross secton area of braces n the jth story, fundamental perod n the th step and the target perod, respectvely. s teraton power, whch s more than zero. Results of ths study ndcate that mnmum teraton steps and fast convergence can be obtaned for equal to. 4. The ZBF structure s excted by a gven earthquake ground moton. Then, the nterstory dsplacement ductlty rato of each story can be computed by dvdng the maxmum elastc nter-story dsplacement demand nto the maxmum nelastc nterstory dsplacement demand. Calculate the coeffcent of varaton (COV) of story ductlty dstrbuton along the heght of the structure and compare t wth the target value of nterest, whch s set here as.5. If the value of COV s less than the presumed target value, no teraton s necessary. Otherwse, total base shear strength must be scaled (by ether ncreasng or decreasng) untl a unform dstrbuton of ductlty rato along the heght of the structure s acheved. As explaned n Equaton (5), due to drect relatonshp between the story shear strength and the area moment of nerta of each story braces, the followng equaton s proposed: max ( I j ) 1.( I j ) ave (7) Where (I j ) s the area moment of nerta of braces n the jth story at the th teraton. s teraton power, whch s more than zero. Results of ths study ndcate that can be consdered from.1 to. whch to large extent depends on to the earthquake ground moton characterstcs. 5. Repeat steps 3 4 for dfferent target perods.. Repeat steps 5 for dfferent earthquake ground motons.. Results and Dscussons.1. Effcency of the unform deformaton theory for ZBF systems As mentoned n the pervous secton, the man objectve of ths study s to decrease the maxmum ductlty rato ( max ) and to acheve the unform ductlty rato () along the heght of the ZBF structures. For ths purpose, 5, 1 and 15 story ZBF models wth the fundamental perods of respectvely.4,. and.8 sec were desgned and thousands of nonlnear dynamc analyses were performed subjected to selected earthquake ground motons. Accordng to the proposed optmzaton algorthm descrbed n the prevous secton, the unform dstrbuton of ductlty rato () along the heght of the ZBF systems can be obtaned through an teratve procedure. Fgure 5-7 show the dstrbuton of ductlty rato () for 5, 1 and 15 story ZBF structures under Landers and Morgan Hll earthquakes.

10 Story Story Story Story 5 J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43-5 Prelmnary answer Fnal answer Story ductlty () Story ductlty () (a) (b) Fgure 5. Dstrbuton of nter-story ductlty demand rato over the heght of 5- story ZBF structure under (a) Landers & (b) Morgan Hll earthquakes. 1 1 Prelmnary answer Fnal answer Story ductlty () Story ductlty () (a) (b) Fgure. Dstrbuton of nter-story ductlty demand rato over the heght of 1- story ZBF structure under (a) Landers & (b) Morgan Hll earthquakes.

11 Story Story J. Vasegh Amr et al./ Journal of Rehabltaton n Cvl Engneerng 3-1 (15) Prelmnary answer Fnal answer Story ductlty () Story ductlty () (a) (b) Fgure 7. Dstrbuton of nter-story ductlty demand rato over the heght of 15- story ZBF structure under (a) Landers & (b) Morgan Hll earthquakes. From these fgure, t s found that the maxmum ductlty rato n ZBF structures s generally occurred n the frs story. The reason of ths result goes back to the hysteretc behavor of ZBF structures. As mentoned earler, the hysteretc behavor of ZBF structures s controlled by the bucklng behavor of compresson braces over the heght of the structure and ths mechansm s ntated from the frst story and wll be extended over the heght of the structure. Therefore, the dstrbuton of damage along the heght of the structure s nonunform and the maxmum damage occurs n the lowest story, whch mples that the ZBF structure cannot exhbt ts maxmum capacty of energy dsspaton. On the other hand, the results of ths study show that by usng the proposed unform deformaton theory the capacty of energy dsspaton n ZBF structures sgnfcantly ncreases as shown n Fgure 8. Results are provded for the mean dstrbuton of ductlty rato () of 5-, 1- and 15-story ZBF structures subject to the 1 records of earthquake ground motons lsted n Table 1. The results demonstrate the effcency of unform deformaton theory for ZBF systems such that the reducton of mean maxmum ductlty ratos ( max ) for 5-, 1- and 15-story ZBF structures are %.1, %55.4 and %5.7, respectvely. Also, the C.O.V (%) of 5-, 1- and 15- story ZBF structures changes from %.7, %7.8 and %5. for the ntal structures to %4.3, %3.3 and %4.4 for optmum structures, respectvely, whch demonstrates the effcency of the proposed algorthm.

12 max & 1 COV Story Story Story 54 J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43-5 Mean of prelmnary answer Mean of fnal answer Story ductlty () Story ductlty () Fgure 8. Dstrbuton of ductlty rato n hgh of the 5-, 1- and 15- story ZBF structures; average of 1 earthquake ground motons Story ductlty ().. Reducton of maxmum damage As mentoned earler, to assess the damage states the maxmum ductlty rato ( max ) can be consdered as damage ndex for ZBF structures. Fgures 9-11 show the varaton of the maxmum ductlty rato ( max ) and COV of stores ductlty rato () over the heght of the structure under Landers earthquake for 5-, 1- and 15- story ZBF structures n each step.the results show that for the structure wth constant structural weght the maxmum ductlty rato ( max ) and COV decrease n each tératon step. Ths mples That generally decreasng the structural damage ndex s always accompaned by reducton of the COV (.e., more unform damage dstrbuton over heght and less global damage). Therefore, the value of COV s drectly related to the optmum lateral load pattern. It can be observed that the reducton amount of the maxmum ductlty rato ( max ) under Landers earthquake for 5-, 1- and 15- story ZBF structures are %47, %7 and %, respectvely story ZBF max 1 COV Step Fgure 9. Varaton of maxmum ductlty rato and COV of 5-story ZBF system under Landers earthquake

13 max & 1 COV max & 1 COV J. Vasegh Amr et al./ Journal of Rehabltaton n Cvl Engneerng 3-1 (15) story ZBF max 1 COV Fgure 1. Varaton of maxmum ductlty rato and COV of 1-story ZBF system under Landers earthquake Step story ZBF max 1 COV Fgure 11. Varaton of maxmum ductlty rato and COV for 15- story ZBF system under Landers earthquake Step.3. Varaton of structural weght The man objectve of the present study s to acheve unform ductlty rato along the heght of the ZBF structures whle the maxmum ductlty rato s decreased and the sesmc weght s remaned constant. It s assumed that the weght of the lateral loadresstng system at each story, W E, s proportonal to the story shear strength, S. Therefore, the total weght of the sesmc resstant system, W E, can be calculated as: W E n 1 W E n 1. S. n 1 S (8) Where, s the proportonng coeffcent. If the values of total sesmc weght of the ZBF structure n ntal and fnal steps are assumed (W E ) I and (W E ) F,respectvely, the relatve weght (RW) wll be defned as:

14 RW RW J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43- ( WE ) RW ( W ) E F I (9) To evaluate the varaton of the ZBF structural weght, the Landers and Morgan Hll earthquakes were selected and the RW values 5-, 1- and 15- story ZBF models were calculated and the results are depcted n Fgure Landers 5-story 1-story 15-story Morgan Hll 5-story 1-story 15-story Fgure 1. Varaton of relatve weght of 5-, 1- and 15- story ZBF structures under Landers and Morgan Hll earthquakes It s clear that when the values of RW are equal to 1, the varaton of structural weght durng the achevement of unform ductlty rato s neglgble, and the structural weght s approxmately constant. The results of Fgure 1 show that the maxmum varatons of RW for 5-, 1- and 15- story ZBF structures are less than %5. It can be concluded that n the present study, the total weghts of the ZBF structures to acheve the unform dstrbuton of ductlty ratos wll be constant, confrmng the concept of the selected damage ndex for the current study..4. Varaton of teraton power () Iteraton power () s a key factor of convergence rate to acheve the unform deformaton along the heght of the structure. In ths study, the ntal value of teraton power () s assumed.1 and, then, durng the teraton process ths factor s automatcally modfed n each step such that the most sutable convergence power can be obtaned. Fgure 13 llustrates the varaton of teraton power () n each step for 1-story ZBF structure under Borrego Mtn, Loma preta and Morgan Hll earthquakes. It s found that: (1) the varaton of teraton power () strongly depends on the characterstcs of each earthquake, () the varaton of the teraton power () pattern s very non-unform when the value s selected greater than.. The reason of the hgh senstvty of the teraton power () may go back to the bucklng behavor of ZBF structures.

15 J. Vasegh Amr et al./ Journal of Rehabltaton n Cvl Engneerng 3-1 (15) Borrego Mtn Loma Preta (1) Morgan Hll Step Fgure 13. Varaton of the teraton power for 1- story ZBF structure under Borrego Mtn, Loma preta (1) and Morgan Hll earthquakes To compare the teraton power () of 5, 1 and 15 stores ZBF models subjected to the 1 earthquake ground motons lsted n Table 1, a column chart was developed. Fgure 14 shows the varaton of mean teraton power for 5, 1 and 15 stores ZBF structures. As a mentoned above, the varaton of teraton power () strongly depends on the characterstcs of each earthquake whle t s observed that n most of earthquakes the mean teraton power () between.1 and. provdes an approprate convergence..5 5 story ZBF.4 1 story ZBF 15 story ZBF Borrego Mtn Kocael (18) Kocael (9) Landers Loma Preta (1) Loma Preta (5) Morgan Hll N. Palm Sprngs (7) N. Palm Vctora Sprngs (3) Fgure 14. Varaton of the mean teraton power for 5-, 1- and 15- story ZBF structures under 1 earthquake ground motons

16 58 J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) Conclusons Ths paper developed a Performance-Based Optmzaton algorthm for Zpper-Braced Frames. Fve- ten- and ffteen-story steel Zpper-Braced Frame (ZPF) systems wth constant structural weght were consdered. Snce the sesmc behavor of ZBF structures and ther structural damages sgnfcantly depend on behavor of story braces, by modfyng the braces characterstcs along the heght of the structure, the stores lateral strength were tuned such that nter-story ductlty ratos over the heght of the structure are dstrbuted more unformly. By usng the proposed optmzaton theory the capacty of energy dsspaton n ZBF structures sgnfcantly ncreases, and consequently the desgned structure would be more cost-effcent compared to correspondng code-based structures.the man objectve of ths study s to obtan unform deformatons and decrease maxmum structural damage n ZBF structures. Accordng to the results of ths study, the followng conclusons are made: An optmzaton algorthm for optmum sesmc desgn of zpper braced frames consderng both nelastc and bucklng behavors has been developed n the present study. The proposed optmzaton procedure s based on the constant structural weght crteron to acheve unform heght-wse dstrbuton of nterstory ductlty rato for decreasng the global structural damage. Results demonstrate the effcency of the proposed algorthm for ZBF systems. The results ndcate that for constant structural weght, structures desgned based on the proposed algorthm experence up to 5% less global ductlty rato (damage) compared wth code-based structures. For the structure havng constant weght the maxmum ductlty rato (µ max ) and COV decrease n each teraton step. Ths mples that generally decreasng the structural damage ndex s always accompaned by reducton of the COV (.e., more unform damage dstrbuton over the heght and less global damage). The varaton of teraton power (µ) strongly depends on the characterstcs of each earthquake whle t s observed that n most of earthquakes, n average, the teraton power (µ) between.1 and. provdes an approprate convergence. Based on the proposed optmzaton algorthm, the varaton of structural weght n ZBF structures s neglgble and can be assumed to be constant durng the achevement of the unform ductlty ratos along the heght of the ZBF structure. Ths result confrms the concept of the selected damage ndex for the current study. References [1] Green, N.B. (1981). Earthquake Resstant Buldng Desgn and Constructon. Second Edton, Van Nostrand Renhold Company, New York. [] Hart, G.C. (). Earthquake forces for the lateral force code. The structural Desgn of Tall Buldngs, Vol. 9, pp [3] Chopra, A.K. (1). Dynamcs of structures, Theory and Applcatons to Earthquake Engneerng. nd Edton, Prentce Hall Inc., London. [4] Mahn, S.A. (1998). Lessons from damage to steel buldngs durng the Northrdge earthquake. Engneerng Structures, Vol., No. 4, pp. 1-7.

17 J. Vasegh Amr et al./ Journal of Rehabltaton n Cvl Engneerng 3-1 (15) [5] Buldng Sesmc Safety Councl (BSSC). Natonal Earthquake Hazard Reducton Program (NEHRP). Recommended Provsons for Sesmc Regulatons for 348 New Buldngs and Other Structures-Part : Commentary (FEMA45 ), Federal Emergency Management Agency, Washngton, D. C, 3. [] IBC (1). Internatonal Buldng Code. Internatonal Code Councl. Country Club Hlls, USA. [7] UBC (1997). Structural engneerng desgn provsons. In: Unform buldng code. Internatonal conference of buldng offcals, Vol.. [8] Park, K., Medna, RA. (7). Conceptual sesmc desgn of regular frames based on the concept of unform damage. Journal of Structural Engneerng (ASCE) 133(7): [9] Chopra, A.K. (1), Dynamcs of structures, Theory and Applcatons to Earthquake Engneerng. 4 th Edton, Prentce Hall Inc., London. [1] Leelatavwat, S., Goel, SC. and Stojadnovc B. (1999). Toward performance-based sesmc desgn of structures. Earthquake Spectra, 15; [11] Lee, SS, and Goel, SC. (1). Performance-Based Desgn of Steel Moment Frames Usng Target Drft and Yeld Mechansm. Report No. UMCEE 1-17, Department of Cvl and nvronmental Engneerng, Unversty of Mchgan, Ann Arbor. [1] Mohammad, RK., El-Naggar, MH., Moghaddam, H. (4). Optmum Strength Dstrbuton for Sesmc Resstant Shear Buldngs. Internatonal Journal of Solds and Structures, 41: [13] Ganjav, B., Vasegh Amr, J., Ghodrat Amr, G., Yahyazadeh Ahmad, Q. (8). Dstrbuton of drft, hysteretc energy and damage n renforced concrete buldngs wth unform strength rato. The 14th World Conference on Earthquake Engneerng, Bejng, Chna. [14] Hajrasoulha, I. and Moghaddam, H. (9). New lateral force dstrbuton for sesmc desgn of structures. Journal of Structural Engneerng (ASCE) 135(8): [15] Goel, SC., Lao, WC., Bayat, MR., and Chao, SH. (1). Performance-Based Plastc Desgn (PBPD) Method for Earthquake-Resstant Structures: An Overvew. Structural Desgn of Tall Specal Buldngs, 19: [1] Mohammad, RK., Ghasemof, A. (15). Performance-Based Desgn Optmzaton Usng Unform Deformaton Theory: A Comparson Study. Latn Amercan of Solds and Structures, Vol. 1. [17] Ganjav, B. and Hao, H., (13). Optmum lateral load pattern for elastc sesmc desgn of buldngs ncorporatng sol structure nteracton effects. Earthquake Engneerng and Structural Dynamcs, 4(): [18] Ganjav, B., (15). Optmal Structural Weght for Flexble-Base Buldngs under Strong Ground Moton Exctatons. Asan Journal of Cvl Engneerng, (In press) [19] Khatb, IF., Mahn, SA., Pster, KS. (1988). SesmcBehavor of Concentrcally Braced Steel Frames, Earthquake Engneerng Research Center. Report no. UCB/EERC-88/1 Unversty of Calforna, Berkeley. [] Tremblay, R., Trca, L. (3). Behavor and Desgn of Mult-Story Zpper Concentrcally Braced Steel Frames for the Mtgaton of Soft-Story Response. n: Proceedngs of the Conference on Behavor of Steel Structures n Sesmc Areas, pp [1] Yang, C., Leon, R., DesRoches, R. (8). Desgn and Behavor of Zpper-Braced Frames. Engneerng Structures, 3, pp [] Sabell, R. (1). Research on Improvng the Desgn and Analyss of Earthquake Resstant Steel-Braced Frames. Earthquake Engneerng Research Insttute, NEHRP Fellowshp Report No. PF-9. Oakland, Calforna.

18 J. Vasegh Amr et al./journal of Rehabltaton n Cvl Engneerng 3-1 (15) 43- [3] ASCE7-1 (1). Mnmum Desgn Loads for Buldngs and Other Structures. Amercan Socety of Cvl Engneers: Reston, VA. [4] Amercan Insttute of Steel Constructon (5). Sesmc Provsons for Structural Steel Buldngs. AISC Sesmc, Chcago. [5] Mazzon, S., McKenna, F., Scott, MH., Fenves, GL. (14). OpenSEES Command Language Manual, Pacfc Earthquake Engneerng Research Center. [] Urz, P., Mahn, S. (4). Summary of test results for UC Berkeley specal concentrc braced frame specmen No. 1 (SCBF-1). [7] SesmoMatch (14). A computer program for adjustng earthquake records to match a specfc target response spectrum. Avalable from: [8] Chandler, A.M., Lam, T.K. (1). Performance-based desgn n earthquake engneerng: a mult-dscplnary revew. Engneerng Structures, No. 3, pp